Through some calculations it's easy to see that
$$(2x - 6,x - 10) = (x - 10, 14) = (x + 4, 14)$$
an so you can also easily prove that the ring you obtain is
$$\mathbb Z_{14}[x]/(x + [4]_{14})$$
and as YACP pointed out this quotient is isomorphic to $\mathbb Z_{14}$.